Speaker
Description
The spectrum of the Dirac operator is not a directly observable object,
however, several bulk thermodynamic quantities can be expressed in terms of
the Dirac spectral density. The most prominent example is the Banks-Casher
relation that connects the order parameter of chiral symmetry breaking to the
Dirac spectrum. Recently, above the crossover temperature, a rich and highly
nontrivial structure has been uncovered in the lowest part of the Dirac
spectrum, the region which is intimately connected to confinement and the
realization of chiral symmetry. In the talk I will cover a selection of these
results. In particular, I will show that the crossover to the high temperature
phase is accompanied by an Anderson-type localization transition of the lowest
part of the spectrum, and at high enough temperature a singular peak appears
in the spectral density. As a result, a reinterpretation of the Banks-Casher
relation is needed. The spectral peak can be fully understood in terms of a
dilute, ideal gas of topological objects which make the chiral limit highly
nontrivial, and are responsible for $U(1)_A$ symmetry remaining broken even
above the crossover temperature.